Seven on Dice Road

In any game using two dice, the number Seven plays a huge role. Backgammon, Parcheesi, Monopoly, and Craps are played best by those who understand and apply the very high likelihood that the number Seven will frequently appear. Frequency of appearance can be understood in both theory and experience, and I recommend both. By theory, I mean the branch of mathematics called probability. By experience, I mean you personally rolling the dice many times and recording for later analysis what those dice showed.

Gaining deep appreciation for the significance of Seven is best achieved in isolation. In the context of playing games, the nuances of the dice outcomes will be overwhelmed by their meaning. Those nuances can and should be appreciated without distractions. Therefore, let’s set games aside for a while and just consider dice.

An essential exercise is to actually roll two dice and record the outcomes. On lined paper, record the sequence of outcomes by making one type of mark for Sevens and just one other type of mark for everything else. Because there are 36 possible dice outcomes for each roll, for a good sample size you should record some reasonably high multiple of that number. 360 rolls are the minimum, and 720 rolls are just fine. You want to have a good look at a sizable slice of Dice Road. Please use quality paper so that you can keep the results for a while.

You may find that using a computer game to generate the dice outcomes will be faster and easier than rolling two physical dice. Computer games have random number generators that are adequate for this educational purpose. You might try Both methods are just fine.

You will need to record the actual sequence of outcomes rather than just the summary totals. What we are examining is far more than just the total number of Sevens that were rolled. We are also deeply interested in the spacing of Sevens along dice road. For example, your sequence might look like: ooooo7oooooooo7oooo7oo77oooooo7oo7oooooooooo7oo.

After you have finished recording the sequence of Sevens and non-Sevens, use a bright color highlighter to mark just the Sevens. After the Sevens are marked, hold the paper at arm’s length and look at the overall picture that the dice have made. I already know what you will see; I am the Alchemist. You will be looking at an undeniable representation of chaos, but what is interesting is that chaos shows up as clusters. You will have clusters of Sevens like bunches of grapes, and you will have long stretches of dice road with no Sevens at all. Sevens will have appeared approximately one-sixth of the total rolls, which is their probability, but they will have done so highly irregularly. That is very important.

Save your results. We’ll consider them again later.


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